Search for heavy neutral leptons in $π^+$ decays to positrons

The NA62 experiment at CERN reports a search for heavy neutral leptons in $\pi^+ \to e^+ N$ decays using 2017–2024 data, establishing upper limits on the mixing element $|U_{e4}|^2$ at the level of $10^{-8}$ for particle masses between 95 and 126 MeV/$c^2$.

The Gist

The Big Picture: Hunting for the "Ghost" Particle

Imagine the Standard Model of physics as a very strict, well-organized library. We know exactly what books (particles) are on the shelves: electrons, protons, neutrinos, etc. But scientists have noticed that the "neutrino" section is missing some pages. We know neutrinos have mass (they aren't weightless ghosts), but the library's original catalog doesn't explain how.

To fix this, a theory called the $\nu$MSM suggests there are hidden, "heavy" cousins of the neutrino called Heavy Neutral Leptons (HNLs). These are like secret agents: they are heavy, they don't interact much with the world (making them hard to find), and they might explain why the universe has more matter than antimatter, or even what Dark Matter is.

The NA62 experiment at CERN decided to play detective to see if they could catch one of these agents in the act.

The Setup: A High-Speed Particle Factory

The experiment is set up in a massive underground tunnel at CERN.

• The Gun: They shoot a beam of protons at a beryllium target. This creates a chaotic spray of secondary particles, mostly pions ($\pi^+$), protons, and kaons ($K^+$).
• The Track: These particles zoom through a vacuum tube (the "decay volume") that is 75 meters long. It's like a high-speed highway where particles are allowed to crash and decay.
• The Camera: Surrounding this highway is a giant, ultra-sensitive detector (the NA62 detector). It's like a high-speed camera system that can track the speed, direction, and energy of every particle passing through, with precision down to the nanosecond.

The Crime Scene: The "Missing" Energy

The scientists are looking for a specific type of "crime": a pion ($\pi^+$) decaying into a positron (a positive electron, $e^+$) and a Heavy Neutral Lepton ($N$).

In the "normal" version of this event (Standard Model), a pion decays into a positron and a regular, invisible neutrino. Because the neutrino is so light, the math works out perfectly.

But if a Heavy Neutral Lepton is involved, it's heavier.

• The Analogy: Imagine you are throwing a ball (the pion) and it splits into a tennis ball (the positron) and a mystery object.
  • If the mystery object is a feather (a normal neutrino), the tennis ball flies one way.
  • If the mystery object is a bowling ball (an HNL), the tennis ball flies a different way and with different energy.

The scientists can't see the HNL directly (it's a "ghost"). Instead, they calculate the "missing mass." They measure the pion's original energy and the positron's final energy. If the numbers don't add up to zero (the expected weight of a normal neutrino), it means something heavy is missing.

The Investigation: Sifting Through the Noise

The challenge is that this "crime" is incredibly rare. For every billion normal decays, maybe only a few involve an HNL. Plus, there is a lot of "noise" (background events) that looks similar.

1. The Filter: The team collected data from 2017 to 2024. They used a computer to filter out the "traffic jams" (background events) where particles just happened to look like the signal by accident.
2. The Search Zone: They focused on a specific weight range for the HNL: between 95 and 126 MeV/c². Think of this as searching for a suspect in a specific height range.
3. The Result: They looked at the "missing mass" data. They found no new peaks. In other words, they didn't find any evidence of the heavy ghost particles in this specific weight range.

The Verdict: Setting the Boundaries

Since they didn't find the HNLs, they didn't say "they don't exist." Instead, they set a limit.

• The Metaphor: Imagine you are fishing in a lake. You cast your net 10,000 times and catch zero goldfish. You can't say goldfish don't exist in the world, but you can say, "If goldfish are in this lake, they must be so rare that my net didn't catch even one."
• The Paper's Claim: The NA62 team established that if these Heavy Neutral Leptons exist in the 95–126 MeV/c² range, they must be extremely rare. Specifically, the probability of a pion turning into a positron and an HNL is less than 1 in 100 million (a mixing parameter of $10^{-8}$).

Why This Matters (According to the Paper)

The paper compares their results to previous experiments (like PIENU).

• The Comparison: The PIENU experiment looked at pions that were stopped and sitting still. NA62 looked at pions flying at high speeds.
• The Outcome: NA62's limits are just as good as, or slightly better than, the previous best limits for this specific weight range.

Summary

The NA62 collaboration built a high-tech particle factory to hunt for a hypothetical heavy cousin of the neutrino. They watched billions of particle decays, looking for a tiny imbalance in energy that would reveal the ghost particle's presence. They didn't find it. However, by not finding it, they successfully drew a tighter line around where these particles could be hiding, telling future physicists: "If you are looking for these heavy neutrinos in this specific weight range, you need to look even harder than we did."

Technical Summary

Technical Summary: Search for Heavy Neutral Leptons in $\pi^+ \to e^+ N$ Decays

Problem and Motivation
While the Standard Model (SM) posits massless neutrinos, experimental evidence of neutrino oscillations necessitates non-zero neutrino masses. The Neutrino Minimal Standard Model ($\nu$MSM) extends the SM by introducing three right-handed neutrinos, known as Heavy Neutral Leptons (HNLs), to explain neutrino masses, dark matter, and baryon asymmetry. HNLs with masses below the kinematic limit of charged pion decay ($m_{\pi^+} - m_e \approx 139$ MeV/$c^2$) can be produced in the decay $\pi^+ \to e^+ N$. The production rate is governed by the HNL mass ($m_N$) and the mixing parameter $|U_{e4}|^2$. This paper reports a search for such HNLs in the mass range of 95–126 MeV/$c^2$, a region where previous constraints were limited or non-existent for in-flight decays.

Methodology
The analysis utilizes data collected by the NA62 experiment at CERN between 2017 and 2024. The experiment employs a 75 GeV/c unseparated secondary beam containing $\pi^+$, protons, and $K^+$ particles. The detector setup includes a beam spectrometer (GTK), a magnetic spectrometer (STRAW) within a vacuum decay volume (FV), a Ring Imaging Cherenkov detector (RICH), and a Liquid Krypton (LKr) electromagnetic calorimeter.

• Event Selection: The search targets the signature of a single positron in the final state, analogous to the SM decay $\pi^+ \to e^+ \nu_e$. Selection criteria require a positively charged track in the STRAW spectrometer with momentum between 5–30 GeV/c, consistent with LKr energy deposits. Particle identification relies on the $E/p$ ratio (0.9–1.1) and RICH signal patterns.
• Normalization and Background: To minimize systematic uncertainties, the analysis uses a data-driven approach. The number of $\pi^+$ decays in the FV ($N_\pi$) is normalized using the observed rate of SM $\pi^+ \to e^+ \nu_e$ decays. Backgrounds, primarily from $\pi^+ \to \mu^+ \nu_\mu$ and $K^+ \to \mu^+ \nu_\mu$ followed by muon decay, are estimated using sidebands in the squared missing mass spectrum ($m^2_{miss}$). The $K^+$ component is scaled based on observed $K^+ \to e^+ \nu_e$ events.
• Search Strategy: The search scans 63 mass hypotheses within the 95–126 MeV/$c^2$ range. For each hypothesis, the number of observed events ($N_{obs}$) is counted in a signal window defined by the local mass resolution ($\sigma_{m^2}$). Expected background ($N_{exp}$) is derived from a polynomial fit to the sidebands. The analysis assumes an HNL lifetime exceeding 50 ns, rendering decays of HNLs within the detector negligible.

Key Contributions

• Extended Mass Coverage: This work extends the search for HNLs in $\pi^+ \to e^+ N$ decays to the 95–126 MeV/$c^2$ mass range using in-flight decays, complementing previous searches at rest (e.g., by the PIENU experiment).
• High-Precision Normalization: The study establishes a robust normalization method using SM leptonic decays to determine the number of parent pions, effectively canceling first-order detector inefficiencies.
• Comprehensive Dataset: The analysis combines data from two distinct operational periods (2017–2018 and 2021–2024), leveraging detector upgrades (specifically the GTK stations) to improve momentum resolution and acceptance.

Results
No significant excess of events over the expected background was observed in the squared missing mass spectrum. Consequently, the collaboration established 90% confidence level (CL) upper limits on the mixing parameter $|U_{e4}|^2$.

• Limits: For HNL masses between 95 and 126 MeV/$c^2$, the upper limits on $|U_{e4}|^2$ are set at the level of $10^{-8}$.
• Comparison: These results are comparable to or more stringent than previous limits established by the PIENU experiment in the overlapping mass region, despite utilizing different experimental techniques (in-flight vs. stopped pions).
• Sensitivity: The single-event sensitivity ($B_{SES}$) and the corresponding mixing parameter sensitivity ($|U_{e4}|^2_{SES}$) were evaluated as functions of mass, showing optimal sensitivity within the defined search window.

Significance
The paper claims that these results represent the most stringent constraints to date on the mixing of heavy neutral leptons with electron neutrinos in the 95–126 MeV/$c^2$ mass range. By assuming a lifetime greater than 50 ns, the study effectively probes the parameter space relevant for HNLs that are stable on the scale of the detector. The authors note that the sensitivity of this analysis is expected to improve with the inclusion of future NA62 data, further tightening constraints on the $\nu$MSM parameter space.